Nunes appeared Monday on "The Story with Martha MacCallum" and addressed the media narrative that some Republicans are coming around to the idea of impeachment.
"I think that's the narrative that the press has been trying to build. And I don't buy anything that is in the mainstream media," Nunes said.
The congressman then went on to take a shot at Romney, without mentioning his name, who admitted to tweeting under an alias this weekend.
"I prefer to get people on the record. ... [W]e have senators who have fake email or fake Twitter accounts that are out tweeting out at midnight," Nunes said. "The last person to do that was James Comey. And so I don't think those people have a lot of credibility."
Romney, one of President Trump’s top Republican critics, on Sunday appeared to confirm the existence of a shadow Twitter account with the name Pierre Delecto.
Romney also took a series of shots at Trump in an interview that aired Sunday on "Axios on HBO," in which he said some of the president’s rhetoric appealed to racism and claiming that, under his leadership, the U.S. was abandoning allied Kurdish fighters in Syria.
Nunes dismissed the impeachment inquiry calling it "phony."
"I'm not sensing anyone here in the House that's building on impeachment because there is no impeachment," Nunes said. "This is a phony impeachment inquiry. They don't have the votes."
Nunes also noted that Republicans do not have access to transcripts, calling that "unprecedented."
"We as Republicans, even on the Intelligence Committee, we do not have access to the transcripts," Nunes said. "This is unprecedented in history. Here, at least the time that I've been here, typically you conduct the interview, the Republicans get the transcript and the Democrats get a transcript and the witness gets a transcript. We're not being given those transcripts any more."